Using upToConstant with complex numbers

[mikeshulman]

In Complex context, it appears that upToConstant still thinks that all constants are real. If the correct answer is 2xy and is checked upToConstant, then 2xy+1 is marked correct, but 2xy+i is marked incorrect.

[Alex-Jordan]

I looked into this a little. The upToConstant checker option inserts an adaptive parameter. So the real issue is whether adaptive parameters handle complex numbers, and according to this comment, they don't:

pg/lib/Value/Formula.pm

Line 190 in 9cefdf9

# to the ORIGINAL correct answer. (This will have to be

I didn't keep thinking about it more though. Maybe they can be elevated to support complex contexts.

I'm not sure what your immediate needs are, but a custom checker could take the student answer and subtract 2xy, then see if both derivatives (wrt x, y) agree with the zero function. Not as nice as with upToConstant, and also might come with more gotchas. But it's what I would do.

[mikeshulman]

As it turns out, I realized after submitting the bug report that I didn't actually need it right now. But it is still surprising that upToConstant doesn't allow complex constants.

[dpvc]

As Alex points out, the upToConstant option currently uses adaptive parameters to handle the constant, and those are limited to real numbers. I've never been all that happy with the adaptive parameter setup, but that's how the original WeBWorK answer checkers worked before MathObjects, and when I developed MathObjects, I included the options available in the legacy answer checkers. The FormulaUpToConstant object was intended to be the better way to do this using MathObjects.

Unfortunately, FormulaUpToConstant also uses adaptive parameters, so has the same limitation. I have written a new version of parserFormulaUpToConstant.pl, attached below as parserFormulaUpToConstant2.pl, that uses a different method to compare the formulas. This works for complex as well as real-valued formulas, and works with multi-variable formulas, and even vector-valued formulas as well. There are some caveats, so do look at the POD documentation for details.

Note that the traditional FormulaUpToConstant object requires the student to explicitly give a +C (or whatever constant they choose), whereas the upToConstant option does not. This new FormulaUpToConstant() allows you to set a requireConstant => 0 on the cmp() method (or in the context flags) that determines whether the student must include +C or not (it is always allowed, but may or may not be required). So this can be used in the situation you had for upToConstant if you don't want to force the +C in the student answer.

parserFormulaUpToConstant2.pl.zip

[mikeshulman]

Thanks! I didn't get a chance to try this out this semester, but I will the next time I teach complex. Do you plan to incorporate this into the main webwork distribution?